The Ion Transition Range of Solar Wind Turbulence in the Inner Heliosphere: Parker Solar Probe Observations

Abstract

The scaling of the turbulent spectra provides a key measurement that allows us to discriminate between different theoretical predictions of turbulence. In the solar wind, this has driven a large number of studies dedicated to this issue using in situ data from various orbiting spacecraft. While a semblance of consensus exists regarding the scaling in the magnetohydrodynamic (MHD) and dispersive ranges, the precise scaling in the transition range and the actual physical mechanisms that control it remain open questions. Using the high-resolution data in the inner heliosphere from the Parker Solar Probe mission, we find that the sub-ion scales (i.e., at the frequency f ∼ [2, 9] Hz) follow a power-law spectrum f α with a spectral index α varying between −3 and −5.7. Our results also show that there is a trend toward an anticorrelation between the spectral slopes and the power amplitudes at the MHD scales, in agreement with previous studies: the higher the power amplitude the steeper the spectrum at sub-ion scales. A similar trend toward an anticorrelation between steep spectra and increasing normalized cross helicity is found, in agreement with previous theoretical predictions about the imbalanced solar wind. We discuss the ubiquitous nature of the ion transition range in solar wind turbulence in the inner heliosphere.

A Novel Method for Estimating the Intrinsic Magnetic Field Spectrum of Kinetic-Range Turbulence

“…Furthermore, other parameters of the plasma, such as plasma beta [48], ion-to-electron heating rate [49,50] and/or effects of outer scale separation [51] may influence the properties of sub-ion scale cascade. Recent PSP observations [24,26] of a young solar wind suggest that the level normalized cross-helicity (imbalance between the counter-propagating Alfvén wave packets) may play a role in the dynamics of the transitional range, which may lead to the observed steepening. Huang et al [26] reported a weak anticorrelation between the transition range spectral index and cross-helicity, in relative terms, such a trend is qualitatively consistent with Figure 8 because higher levels of inertial range fluctuations are characteristic for fast solar wind [52], which exhibits non-zero cross-helicity.…”

“…Recent PSP observations [24,26] of a young solar wind suggest that the level normalized cross-helicity (imbalance between the counter-propagating Alfvén wave packets) may play a role in the dynamics of the transitional range, which may lead to the observed steepening. Huang et al [26] reported a weak anticorrelation between the transition range spectral index and cross-helicity, in relative terms, such a trend is qualitatively consistent with Figure 8 because higher levels of inertial range fluctuations are characteristic for fast solar wind [52], which exhibits non-zero cross-helicity. We plan to address the role of cross-helicity in a future study that will employ hybrid-kinetic simulations and the technique introduced in the current manuscript.…”

“…By keeping the noise slope constant (b = b fit = −0.03), we can compute the asymptotic value (R obs → ∞) for each local slope, that is, the value of an 'intrinsic' local slope that would have been measured in the absence of the noise, s rec = a = (sR obs + b)/(R obs − 1). Furthermore, a few studies [26,42] showed a dependence of the slopes in the transition range on absolute or relative levels of magnetic field fluctuations, δB or δB/B 0 . Let us denote the average P B within the range of the spacecraft frame frequencies 0.05 Hz < f < 0.1 Hz as P in .…”

“…In the power spectral density (PSD) of density, magnetic, velocity, and/or electric fields, the transition manifests itself as a break at the Taylor-shifted (We adopt a concise expression for the Taylor's frozen-in hypothesis that allows a conversion of a temporal measurement, t, to spatial measurement, l: l = V sw t, where V sw is the solar wind speed) spacecraft frame frequency ( f ) of the respective ion characteristic scales [22]. Moreover, a few authors [23][24][25][26] have reported the presence of a double break in the spectra of magnetic field fluctuations: from the inertial range, where the spectrum follows a power law ∝ f α , α ∈ [−1.4, −2] for example, [5,27], it sometimes steepens significantly to f α , α ∈ [−3, −6] [24,26], and then it becomes less steep, ∝ f α , α ∈ [−2.6, −3.2] [28][29][30]. The intermediate range of frequencies where the spectra are steepest is usually denoted as transition range [23].…”

Small-scale Induced Large-scale Transitions in Solar Wind Magnetic Field

“…Several studies have been devoted to the investigation of spectral breaks at both low and high frequencies (e.g., Markovskii et al 2008;Bruno et al 2014Bruno et al , 2017, as well as, to link the location of these breaks to spatial scales in the plasma frame (e.g., Bourouaine et al 2012), mostly related to both ion gyroradius and inertial length (Chen et al 2014). However, various physical processes operate near the observed spectral break (around 1 Hz) such that a direct connection with a peculiar dynamics (e.g., waves vs. instabilities, dispersion vs. damping mechanisms) is really difficult at 1 AU solar distance, thus still remaining an open question (e.g., Alexandrova et al 2013;Huang et al 2021). By searching for scaling-law behaviors and looking at high-order statistics several insights have been provided on turbulence and intermittency (Kolmogorov 1941(Kolmogorov , 1962 as well as on both the direct and inverse energy/enstrophy cascade mechanisms (Matthaeus & Goldstein 1982;Sorriso-Valvo et al 2007).…”